Once you build an interval with the single x at hand

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Unformatted text preview: mate is (3 − 0.1645, 3 + 0.1645) = (2.8355, 3.1645) Question: what does the confidence interval mean? “The probability that µ is in this interval is 90%”? NO! Utku Suleymanoglu (UMich) Interval Estimation 7 / 17 Interval Estimation of Population Mean Interpretation of Confidence Interval Estimates Population parameter, µ, is unchanging. It is not probabilistic. Once you build an interval with the single x at hand, µ is either inside or outside of ¯ it. You don’t know which is the case, but there is no probability to it. So you don’t say “probability that µ is in my CI (2.8355, 3.1645) is 90%”. Correct interpretation of CI’s are related to sampling distributions. Notice L and U ¯ are also functions of X , hence also random themselves. We build different CI’s with different x ’s if we had different samples. ¯ We had kept doing this (repeated sampling), we know that 90% of the CI’s we build will have the correct µ in it. That is why 100(1 − α)% is called the confidence level. NOT because we have 90% probability that µ is inside of the confidence interval we just built. But we are 90% co...
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